She said: “While David Cameron is my Prime Minister, when he comes to Scotland he is not my boss, we are colleagues.

“I hope very much to work with our Prime Minister,” she added. “But if he needs a quiet tap on the shoulder, then I’m just the girl to do it.”

She also appointed David Mundell, Scotland’s only Tory MP, as interim party chairman – a move described by the SNP as a “slapdown for Murdo Fraser”.

While David Cameron is my Prime Ministe

Ruth Davidson

Ms Davidson, a former Territorial Army member and kick boxing enthusiast, will need all her fighting spirit to unite the warring party.

Mr Fraser received 2,096 first preference votes against her 2,278, and he also had the backing of seven MSPs. But the new leader – who also saw off MSPs Jackson Carlaw and Margaret Mitchell – rejected fears of a split.

She said: “They are not my opponents, they are my colleagues. This leadership campaign was enriched by their passion, energy and ideas.”

Ms Davidson also signalled her willingness to stand up to Alex Salmond.

“I don’t envy the SNP,” she said. “They are tasked with making the negative case against the United Kingdom, talking down our history, our country and our achievements.”

After the election result, a visibly devastated Mr Fraser conceded his “bold and radical” plan to scrap the Conservatives had been a “leap too far”.